The key Syrian town of Qusair, near the Lebanon border, has been heavily hit by fierce fighting in recent weeks. Photograph: AP

The Syrian government hailed a strategic victory on Wednesday after the border town of Qusair fell to Hezbollah forces following a siege that pitched the Lebanese Shia militia against several thousand Sunni rebels in what had been billed as a defining battle of the country's civil war.

Rebel groups fighting the regime of President Bashar al-Assad confirmed early on Wednesday that they had pulled out of the town in the early hours, with fighters taking refuge in hamlets near Syria's third city, Homs, 20 miles to the north.

Outgunned since the siege began, rebels inside the town said that they had no option but to flee "in the face of this huge arsenal and lack of supplies and the blatant intervention of Hezbollah".

The fate of residents who remained as the battle raged remains unclear. Rebel leaders from the town who contacted the Guardian earlier this week said more than 15,000 people had stayed in their homes from a prewar population of 30,000.

The International Committee of the Red Cross (ICRC) said it had not been given permission by Damascus to enter the town, despite winning assurances of access earlier in the week.

"We can't give any concrete information on numbers killed, wounded, or remaining in Qusair," an ICRC spokesman said. "We're still in dialogue with the Syrian authorities on reaching Qusair, particularly with a view to getting in medical supplies."

Underlining the difficulty of finding a diplomatic solution to the crisis, the UN's Syria envoy, Lakhdar Brahimi, said that a peace conference that was originally scheduled to be held in Geneva this month would now not take place before July.

Qusair had come under heavy bombardment from artillery and shells dropped by the Syrian air force and rebel supply lines had been severed by regime forces to the north and east while Hezbollah had advanced from the south and west.

Hezbollah has led the attack. Its large-scale role has drawn strident criticism in Lebanon and across the Sunni Arab world, where inter-Muslim sectarian tensions have reached dangerous highs, especially since the assault on Qusair began.

There was no immediate reaction from the Hezbollah leadership, which sources close to the group say is anxious not to appear triumphant in Syria - in contrast to its posture after a clash with Israel.

Media outlets loyal to the group announced that the town had been "cleared of terrorists" at around 6.30am on Wednesday. Hezbollah is believed to have suffered close to 200 casualties during the fighting, a higher number than its members had expected before launching the attack.

On Wednesday Shia residents of the south Beirut suburb of Dahiyah were handing out celebratory sweets at traffic lights to mark the group's victory in Syria - a war zone far from southern Lebanon, where it has battled its traditional foe, Israel, for much of the past 30 years.

Hezbollah's role as a spearhead against a Sunni insurgency in an Arab land has forced a rethink of the group's raison d'etre and has unambiguously wedded it to the fortunes of the Assad regime. The Syrian military had been unable to gain ground in numerous battles across the country until the increased role of Hezbollah and a militia of Shia fighters from Syria and elsewhere, known as Abu Fadl al-Abbas.

Iran, the main patron of both groups, released a statement "congratulating the Syrian people for their victory".

In recent days Hezbollah had deployed hundreds of its elite forces to Qusair, a sign that the battle was drawing to a close despite resistance from rebels that had proved tougher than expected.

The defence of the town was primarily led by homegrown fighters, among them defectors. However, reinforcements from Homs and Aleppo, as well as a contingent of around 200 from the al-Qaida-aligned Jabhat al-Nusra, arrived one week ago. The total number of defenders is thought to have numbered around 3,000.

Rebel casualty figures are unknown. But on Monday, a surgeon from the town contacted the Guardian to say his supplies of vital medicines had run out. "Nothing has been able to get through, he said."